Answer:
[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]
Step-by-step explanation:
Let f(x) be the 3rd degree polynomial function.
The roots of this function are:
x=-2, x=-1 and x=3.
The factored form is:
[tex]f(x) = a(x + 2)(x + 1)(x - 3)[/tex]
This equation passes through (2,12)
This implies that;
[tex]a(2 + 2)(2+ 1)(2 - 3) = 12 \\ - 12a = 12 \\ a = - 1[/tex]
The polynomial function is
[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]
Marcus had 824 marbles and put them equally into 5 bags. How many marbles will be remaining after placing 164 marbles in each bag?
Answer:
The right answer is, 4.
Step-by-step explanation:
Why:
164x5 = 820
So:
824-820 = 4
-2 (3 x - 9 ) + 5x = 10
Answer: × = 8
Step-by-step explanation:
-2 (3 x - 9 ) + 5x = 10
Step 1: Open the bracket
-6× + 18 + 5x = 10
Step 2: Combine like terms
-6× + 5× = 10 -18
-1× = -8
×= -8/-1
×=8
Answer:
x=8
Step-by-step explanation:
Nine out of twelve members of a jury are over 35 years old. What percent of the jury is not over 35?
Answer:
75% are so 15%
Step-by-step explanation:
To determine the percentage of the jury not over 35 years old, divide the number of jurors not over 35 by the total number of jurors (3/12) and then multiply by 100, resulting in 25 percent.
Explanation:If nine out of twelve jurors are over 35, then three out of twelve jurors are not over 35. To find out what percentage of the jury is not over 35, we use the following calculation:
Divide the number of jurors who are not over 35 by the total number of jurors. So we get 3/12.To convert this fraction into a percentage, multiply by 100. So we get (3/12) × 100.Perform the multiplication: 3 × 100 = 300, then divide by 12: 300 / 12 = 25.Therefore, 25 percent of the jury is not over 35 years old.
a picture frame holds a 4-in. by 6-in. photograph. the frame adds a border x inches wide around the three sides of the photo. on the fourth side the frame forms a border that is 3x - 0.5 in. wide. the combined area of the photograph and the frame is 80.5 in^2. write a quadratic equation for the combined area. Then use the quadratic equation formula to find x
Answer:
1. The quadratic equation is 3x² +17.5x - 58.5 = 0
2. The values of x are 2.38 and -8.21, but we only take 2.38 for our problem.
3. The dimensions of the combined area are approximately 6.38 inches and 12.64 inches.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Photograph dimensions = 4 inches * 6 inches
Frame dimensions = x inches * 3x - 0.5 inches
Area of the combined area of the photograph and the frame = 80.5 inches²
2. Write a quadratic equation for the combined area. Then use the quadratic equation formula to find x.
One side of the combined area of the photograph and the frame = 4 + x inches
Second side of the combined area of the photograph and the frame = 6 + 3x - 0.5 inches
Now, we can write the quadratic equation this way:
Combined area of the photograph and the frame = One side * Second side, replacing with the values we know:
80.5 = (4 + x) * (6 + 3x - 0.5)
80.5 = (4 + x) * (5.5 + 3x)
80.5 = 22 + 5.5x + 12x + 3x²
3x² +17.5x - 58.5 = 0
Using the quadratic formula, where, a = 3, b = 17.5 and c = - 58.5, we have:
x = (-b +/- √b² - 4ac)/2a
x = (-17.5 +/- √17.5² - 4 * 3 * -58.5) 2 * 3
x = (-17.5 +/- √306.25 + 702)/6
x = (-17.5 +/- √1,008.25)/6
x = (-17.5 +/- 31.75)/6
x₁ = 14.25/6 = 2.38
x₂ = -49.25/6 = -8.21
We took the value of x₁ because x₂ is negative and we can't have a negative value for the length or the width, therefore:
80.5 = (4 + x) * (5.5 + 3x)
Replacing x, we have:
80.5 = (4 + 2.38) * (5.5 + 3 * 2.38)
80.5 = 6.38 * 12.64
80.5 ≅ 6.38 * 12.64
For f(x) = 2x+1 and g(x) = x+14, find (gof)(x).
Answer: OPTION B
Step-by-step explanation:
You can observe that the exercise provides you two Linear functions.
The first Linear function is the function f(x). This is:
[tex]f(x) = 2x+1[/tex]
And the other Linear function is the function g(x):
[tex]g(x) = x+14[/tex]
In order to find [tex](gof)(x)[/tex], you need to follow these steps shown below:
Step 1:
You must substitute the function f(x) into the function g(x); this means that the function f(x) will be in the place of the variable "x" of the function g(x); as you can observe below:
[tex](gof)(x) = (2x+1)+14[/tex]
Step 2:
Finally you must combine the like terms (You can notice that the like terms are 1 and 14; then you must add them). Therefore, you get that [tex](gof)(x)[/tex] is:
[tex](gof)(x) = 2x+1+14\\\\(gof)(x) = 2x+15[/tex]
Solid A is similar to solid B. Solid B has a volume of 23000 cubic meters. By what scale factor can you multiply every side of solid A to get solid B if the volume of solid a is 23 cubic meters
Answer:
1,000
Step-by-step explanation:
23,000 divided by 23 is 1,000
I'm really confused about this question about Solving Systems by Elimination
x-y=8
x+y=12
Answer:
x=10
y=2
Step-by-step explanation:
1)add the equations and find what x is.
x-y=8
+x+y=12
—————
2x=20
— —
2 2
x=10
3)fill in x for the second equation.
x+y=12
since x=10,replace x with 10.
10+y=12.
subtract 19 from both sides.
10+y=12
-10 -10
—————-
y=2
express 0.29 as a fraction
Answer:
29/100
Step-by-step explanation:
Answer: 29/100
Step-by-step explanation:
The 2 is in the Tenth place
The 9 is in the Hundredths place
so get 29/100
Example: .5 as a fraction
Answer: 5/10
hi! can anyone help me pls?
Answer:
Option B, -4 and 4
Step-by-step explanation:
Step 1: Subtract 15 from both sides
y^2 - 1 - 15 = 15 - 15
y^2 - 16 = 0
Step 2: Factor
y^2 - 16
(y + 4)(y - 4)
Step 3: Find the solutions
y + 4 - 4 = 0 - 4 and y - 4 + 4 = 0 + 4
y = -4 and y = 4
Answer: Option B, -4 and 4
Answer:
-4 and 4
Step-by-step explanation:
All you need to do is solve for y
[tex]y^{2} - 1 = 15\\[/tex] (plus 1 to both sides)
[tex]y^{2} = 16[/tex] (take square root of 16)
[tex]y = \sqrt{16}[/tex]
[tex]y = +-4[/tex] (whenever you to the root of a perfect square you want the positive and negative root)
To double check if your answer is right: plug in -4 and +4 in as y and see if it equals 15
1. [tex](4)^{2} - 1 =15[/tex]
[tex]16-1 = 15\\15= 15[/tex]
(positive 4 checks out)
2. [tex](-4)^{2} - 1 = 15[/tex]
[tex]16 - 1 = 15\\15 = 15[/tex]
( negative 4 checks out)
How do yo solve (x-5)(-3)=18
Answer:
x = -1
Step-by-step explanation:
Given
(x - 5)(-3) = 18
Expand the bracket
x X -3 -5 x -3 = 18
-3x + 15 = 18
Subtract 15 from both sides
-3x + 15 - 15 = 18 - 15
-3x = 3
Divide both sides by -3
-3x/-3 = 3/-3
x = -1
Guys please help me with #8 and #11 thank you
What is the product of 4.6 and 3 written in word form?
Answer: Thirteen and Eight tenth
Step-by-step explanation:
Product means multiplication
From the question, 4.6 x 3 = 13.8
Solve for x.
x/6 = 2
x=___________
Answer:
12
Step-by-step explanation:
x/6 = 2
x = 6×2 = 12
Answer:
X=12 (sorry for the handwriting)
Convert 2.19 liters to milliliters.
Enter your answer in the box.
2.19 L =
mL
Answer:
2.19 liters = 2190 milliliters
Step-by-step explanation:
4. Carter has one $20 bill, one $10 bill,
four $5 bills and two $1 bills. Aubrey has
two $10 bills, five $5 bills, and seven
$1 bills. Who has more money? Explain.
Answer: Therefore, They both have the same amount!
Step-by-step explanation:
Carter= 20+10+4(5)+2(1)=
30+20+2= 52 dollars
Aubrey= 2(10)+5(5)+7(1)=
20+25+7=52 dollars
Please mark brainliest!
How should the decimal point in 52.48 be moved to determine the product 52.48×10 to the power of 5?
Enter your answers in the boxes to correctly complete this statement.
The decimal point should be moved ___ places to the right because there are ___ zeros in 10 to the power of 5.
Decimal point moved 5 places to the right, since 10⁵ has 5 zeros in it.
Step-by-step explanation:
52.48 is multiplied by 10 to the power of 5, that is 100, 000, we will get ,
[tex]52.48 \times 10^{5}=5248000.00[/tex]
When 52.48 is multiplied by 100,000, we will get 5248 followed by 5 zeros, 524800000.
Now we have to count the decimal point from left to right, so we will get 5248000.00, zeros after the decimal point has no value.
The decimal point should be moved _5__ places to the right because there are _5__ zeros in 10 to the power of 5.
the cube and rectangular prism have the same base area and height. how can you use this information to determine the volume of the pyramid?
The given pyramid's volume is 40 cubic units.
Step-by-step explanation:
Step 1:
It is given that base areas of the pyramid and the prism are the same. The height is also equal.
The rectangular prism's height is 15 units so as per the given question, the height of the pyramid is also 15 units.
Step 2:
The volume of this pyramid is obtained by multiplying [tex]\frac{1}{3}[/tex] with the product of the pyramid's length, width, and height.
For the given pyramid, length = 2 units, width = 4 units and the height = 15 units.
The pyramid's volume [tex]= \frac{1}{3} (length)(width)(height)[/tex] = [tex]\frac{1}{3} (2)(4)(15) = \frac{1}{3} (120)[/tex] = 40 cubic units.
So the volume of the given pyramid is 40 cubic units.
Help with this and I’ll mark you as brainliest ❤️
Answer:
The answer is C
Step-by-step explanation:
Because 1 is 90 because it shaped like a L 2 is 45 because its narow, and 3 is the smallest of them all. I also did it before
determine whether the quadrilateral is a parallelogram justify your answer.
Step-by-step explanation:
Yes, it is a parallelogram because the opposite angles are congruent
Option C
Answer:
yes opposite angles are congruent.
Step-by-step explanation:
On both sides 36 and 144 are congruent or equal
Select the correct answer. Zara is six months into her first job, and she’s also attending community college. She is planning to start saving a portion of her paycheck and has created a monthly budget to track her spending. Which budget item should Zara reduce to increase her savings? A. college tuition B. dining out C. rent D. utility bills
Answer:
B.Dining out
Step-by-step explanation:
A, C, and D are very important and without those she would be in big trouble. She does not need to dine out. Instead of dining out she can go to a normal grocery store and buy cheap food there.
Answer:
It would be DINNING OUT.
Step-by-step explanation:
Because it is something you can stop paying for and save money on. It is a variable expense.
I NEED HELP ASAP PICK ALL
Answer:
Where is the question
Step-by-step explanation:
In a class of 50 students,27 are athletes 9 are musicians and 6 of the musicians are athletes . If one student is randomly selected from the class , find the probability of choosing an athlete or a musician
Answer: 0.6
Step-by-step explanation:
Total population of class = 50
There are 27 athletes, and 9 musicians However, 6 of the musicians are also athletes.
Therefore, totals for athletes and musicians are:
27 + 9 -6 = 30
Thus, the probability of choosing an athlete or a musician is 30/50= 0.6
We could also use the formula:
P(A or M) = P(A) + P(M) - P(A and M)
P(A or M)=27/50+9/50-6/50
P(A or M)=30/50=0.6
I hope this helps!
I NEED HELP ASAP CORRECT ANSWERS ONLY
write the equation of a function that passes through these points
Answer:
heine is a former member and the chief of the United nations and th t in my experience with the United states and t the u.s. government of th world and is th American standard bible in a very good country of th I think 8is the most popular among women and the men in a society where the oth was the other one that had the most of t to the world that I would not like you to be in my life and I don't know how much I
Cullen is 10 years younger than Ada. The product of their ages 2 years ago was 39.
Answer:
15
Step-by-step explanation:
The age cullen is 5 yrs and Ada is 15 years old.
What is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
Cullen is 10 years younger than Ada.
The product of their ages 2 years ago was 39.
let the age of ada be x
Cullen's age = x- 10
22 years ago there age will be
Ada = x-22
Cullen = x-32
Now, the product of their age is 39
(x-2)(x-12)=39
x²-12x-2x + 24=39
x² -14x + 24=39
x² - 14x -15 = 0
x² -15x + x- 15=0
x(x-15) + 1(x-15)=0
(x-15)(x-1)=0
x= 15 or -1.
Hence, the age of Ada is 15 yrs and cullen age is 5.
Learn more about algebra here:
https://brainly.com/question/13715639
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Find the volume of the cylinder.
Either enter an exact answer in terms of it or use 3.14 for T.
with a height of 5 and a radius of 2
Answer:
V=62.8
Step-by-step explanation:
3.14(2)^2(5)
3.14(4)(5)
12.56(5)
62.8
Question is;
Find the number of roots/solutions for the quadratic equation: x^2 + 4 = 0
Unsure about how to figure that out, as we don't have bx. Please help
Answer:
(x-2)(x+2)
Step-by-step explanation:
if we expand the above quadratic we can see that the -2x and + 2x will cancel eachother out therefore there is no bx in this quadratic equation
Answer:
No roots/solutions
Step-by-step explanation:
No bx means b = 0
B² - 4AC
(0)² - 4(1)(4)
-16 < 0
What is the coefficient of x in the expression?
6x + 9y + 15z
A) 3
B) 6
C) 9
D) 15
Answer:
The coefficient is the number before x. So it is 6.
Answer:
Step-by-step explanation:
the answer is B) 6
26. Adrian has a cube that has a volume of 64
cubic centimeters. Which is the surface area of
Adrian's cube?
A. 6 square centimeters
B. 16 square centimeters
C. 32 square centimeter
D. 96 square centimeters
Answer:
Bend down
Step-by-step explanation:
Bebebe
Find the exact valued the function f(x)=6•4^x fox x=-2
Answer:
f(-2) = 3/8
Step-by-step explanation:
f(x)=6•4^x
Let x=-2
f(-2) = 6 * 4^-2
The negative in the exponent means it goes to the denominator
f(-2) = 6 * 1/ 4^2
= 6/4^2
=6/16
Simplifying
=3/8